We report a series of experiments that use a navigation task in which instructions for navigating in a space displayed as grids on a computer screen are given to subjects who then attempt to follow them by mouse clicking on the grids. The navigation task was broken down into component dimensions (e.g., presentation mode of the instructions, length of the instructions, characteristics of the display, size of the grids, response type). For each task dimension, one condition was used at training and the same or another condition was used at test. Each task dimension was examined in terms of two measures. One measure provided an index of transfer (i.e., better performance at test than at training when test and training involved different conditions), and the other provided an index of specificity (i.e., better performance at test when training and test conditions were the same than when training and test conditions were different). By and large, these two indices were complementary, so there was evidence of either transfer or specificity but not both. For one dimension transfer but no specificity was evident, and for another dimension specificity but no transfer was evident. For the remaining dimensions, however, there was asymmetrical transfer, with transfer evident for some conditions and specificity evident for others. The findings are interpreted within the procedural reinstatement framework. They have practical implications concerning how to optimize training and how much fidelity to the testing situation is necessary when training.